On computation of stabilizing loop gain and delay ranges for bi-proper delay systems
Binh Nguyen Le1, Qing-Guo Wang1, Tong Heng Lee1
1Department of Electrical and Computer Engineering, National University of Singapore, 119260 Singapore.
ISA Transactions
|December 3, 2014
Summary
This study develops a general method to precisely calculate stabilizing gain and delay ranges for bi-proper processes. This extends previous graphical techniques to handle complex systems previously excluded from analysis.
Area of Science:
- Control Systems Engineering
- Process Control
- Systems Theory
Background:
- Existing graphical methods for computing stabilizing gain and delay ranges apply to strictly proper processes.
- Bi-proper processes present unique challenges, including non-zero gain at infinite frequency, complicating stability analysis.
- These complications lead to infinite intersections of boundary functions within finite delay ranges, hindering exact computation.
Purpose of the Study:
- To develop a general method for exactly computing stabilizing loop gain and delay ranges for bi-proper processes.
- To address the complications arising from the unique phenomena of bi-proper systems.
- To provide an exact and complete set of loop gain and delay for closed-loop stabilization.
Main Methods:
- Extension of the D-decomposition graphical method to accommodate bi-proper processes.
- Analysis of system behavior at infinite frequency for bi-proper systems.
- Development of techniques to handle infinite intersections of boundary functions.
Main Results:
- A general method is developed that accurately computes stabilizing gain and delay ranges for bi-proper processes.
- The method successfully addresses the challenges posed by non-zero gain at infinite frequency.
- The exact and complete set of loop gain and delay for closed-loop stabilization is determined.
Conclusions:
- The developed method provides an exact and complete solution for stabilizing bi-proper processes, overcoming limitations of prior approaches.
- This work extends the applicability of graphical methods to a broader class of process systems.
- The findings are crucial for robust control design in systems exhibiting bi-proper characteristics.
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